Some puzzles

Summat non-political, non-football related for a change and because I'm bored in the office. A few brainteasers which generally prompt debate (i.e. argument):

1. You're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host (who knows what's behind the doors) opens another door, say No. 3, which has a goat. He then says to you, "Do you want to swap from door 1 to door 2?" Should you switch?

2. A standard jumbo jet is placed on a runway which is actually a treadmill. The treadmill acts in the opposite way to the plane is facing and builds to the takeoff speed of the plane as the pilot goes through the takeoff routine. Does the plane take off?

3. There are 2 sets of 5 cards on a table - set 1 and set 2. Each set is from a different, randomly shuffled deck. Your friend looks at set 1 and says "at least one of these cards is an ace". He looks at set 2 and says "one of these cards is the ace of spades." You are then offered the chance to bet on which set contains 2 or more aces. Which set should you bet on?

4. There is a virus which affects 1 in 10,000 people completely at random. It is entirely symptomless until you suddenly drop dead. Doctors develop a test which is 99% accurate. You take the test and it comes back positive. How worried should you be?

 

Were you at my last job interview?

This is uncanny.

 

I do interview but I can't remember asking any of these, what was it for?

 

Ant a clue to any ov em

 

Not sure if my logic is right but I'd go
1 Swap. Odds were 2/1 initially but are now evens if you swap
2. I reckon the updraft might cause it to lift off.
3. Set 2 could contain all 4 aces, set one only has one
4.its still 100/1 that you're infected so shouldn't be unduly worried although I would be.

 

I got the wording wrong on 3, set 1 is said to contain at least one ace rather than just one ace

 

1. It's 50/50 either way. I'd stick with my first choice.
2. I don't think the plane takes off. And definitely not if it's going to China.
3. Makes no odds. It's one ace in each hand with the same odds on each side... isn't it?
4. Not a bit. You could drop down dead from any number of things before the virus gets you - if it ever does.

 

Surely its 99/1 that you're not infected so should be very worried, if there is only a 1% chance that the test isn't wrong?

 

Who gives a f**k

 

I'm crap with stuff like this. Especially odds

But I don't think the plane would take off cos there would be no wind resistance.

Either that or 20,251. Final answer.

 

I've give it a go
No 1 - stick with original game show host trying a double bluff
No 2 - a plane needs thrust to take off so it wouldn't take off
No 3 - set 1 has more than set 2 due to him saying at least 1 is an ace
No 4 - it doesn't say what the test is for so not overly worried

 

Pane wont take off as no air is passing over the wings.

As I understand it. For a plane to fly, the air travelling over the top of the wing has to travel faster due to increased surface area (curved part of wing) than that below the wing. This creates a pressure difference between the air above the wing (less pressure) and the pressure below wing (greater pressure). The greater the pressure difference the more lift plane has.

 

1. Although probability would suggest not changing in simulation the right answer is to swap which results in an improvement in the likelihood of winning a prize. The argument based on it being a 1 in 3 choice at the outset and 1 in 2 after the first goat is revealed.

 

1. I know that you're supposed to change because it's now 50/50 but that is assuming you are not thinking isn't it? If he says "do you want to change" you're supposed to but if he says "right, round 2. Now which so you want?" It's still 50/50 so if you say I'll keep this one you've made a 50/50 choice. Same question, different wording.

2. The plane takes off. Wheels in contact with the floor have very little to do with a plane taking off

 

1. Regardless of which way the question is phrased your chances are 1/3 of you stick and 2/3 if you switch.

2. Correct

 

My bad. I completely missed the part that said the host knew what was behind the doors. If he didn't know then it would be a 50/50 in round 2. Because he knew and was deliberately showing you a losing door then yes your odds are 1/3.

The third question I haven't a clue about and I know the fourth is a much lower number than you think due to false positives and all that stuff but I'm not smart enough to do the maths

 

Lisa Stansfield

 

No 2 wrong!! If the conveyor speed matches take off speed the plane is stationary. Therefore no air is passing over the wings so no lift!! Same reason planes take off and land into the wind where possible. Lower ground speed required to achieve take off lift.

 

That doesn't make sense. If you are running on a treadmill and the treadmill is going in the opposite direction at the same speed as you are running, you are still running. If you slowed down or stopped you'd fly off! The plane is going in the opposite direction to the treadmill runway so there would be lift.

 

The wheels aren't what is making the plane move forwards, all they're their for is to create less from the ground so the plane willl move regardless

Think about a water plane. They don't have wheels that drive them forwards, they have ski's that let them glide. What makes the plane move is the thrust of the engine pushing it forwards.